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EFFECTIVE SLIP LENGTH: SOME ANALYTICAL AND NUMERICAL RESULTS

Part of:Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  25 August 2015

XINGYOU (PHILIP) ZHANG,
NAT J. LUND and
SHAUN C. HENDY
XINGYOU (PHILIP) ZHANG*
Affiliation:
Computational and Data Sciences, Callaghan Innovation, PO Box 31-310, Lower Hutt5040, New Zealand email philip.zhang@callaghaninnovation.govt.nz
NAT J. LUND
Affiliation:
Department of Physics, Victoria University of Wellington, PO Box 600, Wellington 6140, New Zealand email natjlund@gmail.com
SHAUN C. HENDY
Affiliation:
Department of Physics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand email shaun.hendy@auckland.ac.nz
*
✉philip.zhang@callaghaninnovation.govt.nz
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Abstract

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More and more experimental evidence demonstrates that the slip boundary condition plays an important role in the study of nano- or micro-scale fluid. We propose a homogenization approach to study the effective slippage problem. We show that the effective slip length obtained by homogenization agrees with the results obtained by the traditional method in the literature for the simplest Stokes flow; then we use our approach to deal with two examples which seem quite hard by other analytical methods. We also include some numerical results to validate our analytical results.

Keywords

Stokes floweffective slip lengthhomogenizationanisotropic slipfinite element method

MSC classification

Primary:35Q35: PDEs in connection with fluid mechanics

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 57 , Issue 1 , July 2015, pp. 79 - 88
Copyright
© 2015 Australian Mathematical Society 

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